Page:Poincare Goettingen En.djvu/5

 if you will, to be wholly modern. B notes the moment of reception and this will be the starting time for both chronometers. But it takes a certain time for the signal to go from Paris to Berlin; it travels only with the speed of light. B's watch would therefore be slow. B is too intelligent not to take this into account, and he proceeds to remedy it. The thing seems very simple. They cross signals, A receiving and B sending; they take the mean of the corrections thus made and so have the exact time.

But is this certain? We are assuming that it takes the signal the same time to go from A to B as from B to A. Now A and B are carried along in the motion of the earth with reference to the ether, the vehicle of the electric waves. When A has sent his signal it flies on before him, B moving away in the same way, and the time employed will be longer than if the two observers were at rest. If, on the other hand, it is B who sends, and A who receives, the time is shorter because A goes to meet the signal. It is absolutely impossible for them to know whether or not their chronometers mark the same time. Whatever the method employed, the troubles remain the same. The observation of an astronomic phenomenon and all optical methods run against the same difficulties. B can never know more than an apparent difference of time, more than a species of local hour. The principle of relativity applies completely.

In the old mechanics, however, we prove with this principle all the fundamental laws. We might be tempted to take up the classic arguments and reason as follows. Suppose again two observers, A and B, to call them what we always call two observers in mathematics. Suppose them in motion, going away from each other. Neither can surpass the velocity of light; for example let B go at the rate of 200,000 kilometers toward the right, A of 200,000 kilometers toward the left. A may think himself at rest, and